Report of the fit

Fit summary

Description: Test fit with the MAP 2021 parameterisation.
Minimiser: ceres
Random seed: 1234
Maximum values allowed for q_T / Q for Drell Yan dataset: 0.2 (0.2 for ATLAS dataset)
Maximum values allowed for q_T / Q for SIDIS dataset: min[ min[ 0.2 / z, 0.5 ] + 0.3 / (z*Q) ], 1 ]
Percentile cut: 5
Parameterisation: MAP22g52
Initial parameters fluctuations: False
Explicit formula:

f_{\rm NP}(x,\zeta, b_T)= \exp(S_{\rm NP}(\zeta, b_T))\frac{g_1(x) \exp( - g_1(x) \frac{b_T^2}{4}) + \lambda^2 g_{1B}^2(x) ( 1 - g_{1B}(x) \frac{b_T^2}{4}) \exp( - g_{1B}(x) \frac{b_T^2}{4}) + \lambda_2^2 g_{1C}(x) exp( - g_{1C}(x) \frac{b_T^2}{4}) }{ g_1(x) + \lambda^2 g_{1B}^2(x) + \lambda_2^2 g_{1C}(x) }D_{\rm NP}(z,\zeta, b_T)= \exp(S_{\rm NP}(\zeta, b_T))\frac{g_3(z) \exp( - g_3(z) \frac{b_T^2}{4z^2}) + \frac{\lambda_F}{z^2} g_{3B}^2(z) \big ( 1 - g_{3B}(z) \frac{b_T^2}{4z^2} \big ) \exp( - g_{3B}(z) \frac{b_T^2}{4z^2}) }{ g_3(z) + \frac{\lambda_F}{z^2} g_{3B}^2(z) }S_{\rm NP} = \exp\left[ - g_2^2 \frac{b_T^2}{4} \log \big (\frac{\zeta}{Q_0^2}\big ) \right]g_{1,1B,1C}(x) = N_{1,1B,1C} \frac{x^{\sigma_{1,2,3}}(1-x)^{\alpha^2_{1,2,3}}}{\hat{x}^{\sigma_{1,2,3}}(1-\hat{x})^{\alpha^2_{1,2,3}}}g_{3,3B}(z) = N_{3,3B} \frac{(z^{\beta_{1,2}}+\delta^2_{1,2})(1-z)^{\gamma^2_{1,2}}}{(\hat{z}^{\beta_{1,2}}+\delta^2_{1,2})(1-\hat{z})^{\gamma^2_{1,2}}}Q_0^2 = 1\;{\rm GeV}^2\hat{x} = 0.1\hat{z} = 0.5 t_0 prescription: True

g_2 N_1 \alpha_1 \sigma_1 \lambda N_3 \beta_1 \delta_1 \gamma_1 \lambda_F N_{3B} N_{1B} N_{1C} \lambda_2 \alpha_2 \alpha_3 \sigma_2 \sigma_3 \beta_2 \delta_2 \gamma_2
0.291359102894169 0.2006002300752988 2.773582645534533 2.248567120592055 15666.29847468401 0.005080413995163261 7.921481547106262 0.04015419519659606 1.689458640435588 0.3739836783648748 0.1252334678836607 0.001198114771497247 6.192499833953308e-05 0.005345028327068614 10.25646456703343 2.925229330146624 2.335206033389119 12.53681050529197 2.587650914497618 0.2206893632340438 1.102709259848706

Theory summary

Collinear PDF set: MMHT2014nnlo68cl member 0
Collinear FF set: DSS14_NLO_Pip member 0
Collinear FF set: DSS14_NLO_Pim member 0
Collinear FF set: DSS17_NLO_KaonPlus member 0
Collinear FF set: DSS17_NLO_KaonMinus member 0
b^* prescription: bstarmin
Perturbative order: N3LL
Reference value of the fine-structure constant: \alpha(Q = 91.1876\;{\rm GeV}) = 0.00776578395589 (running True)

Global statistical estimators

N_{rep} = 237
\chi_{0}^2 = 0.9737
\chi_{mean}^2 = 0.9737
\langle\chi^2\rangle \pm \sigma_{\chi^2} = 0.9954 \pm 0.0107
\langle E \rangle \pm \sigma_{E} = 1.9645 \pm 0.129

Parameters

Parameter Central replica Average over replicas Fixed
g_2 0.2913591 0.2851962 \pm 0.02437613 False
N_1 0.20060023 0.28205029 \pm 0.08701141 False
\alpha_1 2.7735826 2.69269837 \pm 0.42011436 False
\sigma_1 2.2485671 1.96123427 \pm 0.67899603 False
\lambda 15666.298 10751.45710149 \pm 10695.31492706 False
N_3 0.005080414 0.00507925 \pm 5.787e-05 False
\beta_1 7.9214815 7.92304252 \pm 0.03860489 False
\delta_1 0.040154195 0.04016474 \pm 0.0002053 False
\gamma_1 1.6894586 1.68917387 \pm 0.00937609 False
\lambda_F 0.37398368 0.37384349 \pm 0.00209969 False
N_{3B} 0.12523347 0.12523011 \pm 0.00050366 False
N_{1B} 0.0011981148 0.00334597 \pm 0.00328188 False
N_{1C} 6.1924998e-05 0.00052578 \pm 0.00211779 False
\lambda_2 0.0053450283 0.00480986 \pm 0.0072475 False
\alpha_2 10.256465 8.93846376 \pm 3.03517724 False
\alpha_3 2.9252293 2.57758165 \pm 1.11551289 False
\sigma_2 2.335206 2.26840233 \pm 1.96175461 False
\sigma_3 12.536811 13.14828391 \pm 2.94856557 False
\beta_2 2.5876509 2.58687529 \pm 0.01989373 False
\delta_2 0.22068936 0.22068596 \pm 0.00080095 False
\gamma_2 1.1027093 1.10249264 \pm 0.00206092 False
Fitted parameter correlation matrix

Fit properties

Global \chi^2 distribution
Global error function distribution
g_2 distribution
N_1 distribution
\alpha_1 distribution
\sigma_1 distribution
\lambda distribution
N_3 distribution
\beta_1 distribution
\delta_1 distribution
\gamma_1 distribution
\lambda_F distribution
N_{3B} distribution
N_{1B} distribution
N_{1C} distribution
\lambda_2 distribution
\alpha_2 distribution
\alpha_3 distribution
\sigma_2 distribution
\sigma_3 distribution
\beta_2 distribution
\delta_2 distribution
\gamma_2 distribution

Table of \chi^2’s

Central-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 1.168 0.227 1.395
E605_Q_8_9 8 2.197 0.131 2.328
E605_Q_10.5_11.5 10 0.419 0.032 0.451
E605_Q_11.5_13.5 12 0.636 0.29 0.926
E605_Q_13.5_18 13 1.004 0.657 1.661
E772_Q_5_6 4 1.209 0.482 1.691
E772_Q_6_7 5 0.995 0.3 1.295
E772_Q_7_8 6 2.41 0.984 3.394
E772_Q_8_9 6 2.318 1.04 3.357
E772_Q_11_12 9 0.959 0.02 0.979
E772_Q_12_13 10 1.188 0.004 1.192
E772_Q_13_14 7 2.455 0.364 2.818
E772_Q_14_15 6 0.284 0.002 0.285
E288_200_Q_4_5 4 0.33 0.122 0.451
E288_200_Q_5_6 5 1.365 0.109 1.474
E288_200_Q_6_7 6 0.2 0.167 0.367
E288_200_Q_7_8 7 0.209 0.15 0.359
E288_200_Q_8_9 8 0.49 0.148 0.638
E288_300_Q_4_5 4 0.566 0.0 0.566
E288_300_Q_5_6 5 1.171 0.0 1.172
E288_300_Q_6_7 6 0.516 0.002 0.518
E288_300_Q_7_8 7 0.058 0.001 0.059
E288_300_Q_8_9 8 0.984 0.005 0.988
E288_300_Q_11_12 9 0.305 0.037 0.342
E288_400_Q_5_6 5 0.619 0.102 0.721
E288_400_Q_6_7 6 0.234 0.092 0.326
E288_400_Q_7_8 7 0.037 0.102 0.139
E288_400_Q_8_9 8 0.757 0.101 0.857
E288_400_Q_11_12 11 0.595 0.045 0.64
E288_400_Q_12_13 12 0.902 0.022 0.924
E288_400_Q_13_14 12 0.751 0.051 0.802
PHENIX_200 2 2.781 1.832 4.613
STAR_510 7 1.417 0.025 1.443
CDF_RunI 25 0.521 0.058 0.579
CDF_RunII 26 0.926 0.003 0.929
D0_RunI 12 0.647 0.028 0.675
D0_RunII 5 1.021 0.459 1.481
D0_RunIImu 3 3.753 0.284 4.037
LHCb_7TeV 7 1.47 0.271 1.741
LHCb_8TeV 7 0.581 0.067 0.648
LHCb_13TeV 7 1.281 0.038 1.32
CMS_7TeV 4 2.265 0.095 2.361
CMS_8TeV 4 1.98 0.001 1.981
CMS_13TeV_y_0_0.4 14 0.465 0.04 0.505
CMS_13TeV_y_0.4_0.8 14 0.323 0.026 0.349
CMS_13TeV_y_0.8_1.2 14 0.513 0.009 0.522
CMS_13TeV_y_1.2_1.6 14 0.22 0.0 0.22
CMS_13TeV_y_1.6_2.4 14 0.392 0.01 0.402
Total 412 0.84 0.133 0.974
Mean-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 1.168 0.227 1.395
E605_Q_8_9 8 2.197 0.131 2.328
E605_Q_10.5_11.5 10 0.419 0.032 0.451
E605_Q_11.5_13.5 12 0.636 0.29 0.926
E605_Q_13.5_18 13 1.004 0.657 1.661
E772_Q_5_6 4 1.209 0.482 1.691
E772_Q_6_7 5 0.995 0.3 1.295
E772_Q_7_8 6 2.41 0.984 3.394
E772_Q_8_9 6 2.318 1.04 3.357
E772_Q_11_12 9 0.959 0.02 0.979
E772_Q_12_13 10 1.188 0.004 1.192
E772_Q_13_14 7 2.455 0.364 2.818
E772_Q_14_15 6 0.284 0.002 0.285
E288_200_Q_4_5 4 0.33 0.122 0.451
E288_200_Q_5_6 5 1.365 0.109 1.474
E288_200_Q_6_7 6 0.2 0.167 0.367
E288_200_Q_7_8 7 0.209 0.15 0.359
E288_200_Q_8_9 8 0.49 0.148 0.638
E288_300_Q_4_5 4 0.566 0.0 0.566
E288_300_Q_5_6 5 1.171 0.0 1.172
E288_300_Q_6_7 6 0.516 0.002 0.518
E288_300_Q_7_8 7 0.058 0.001 0.059
E288_300_Q_8_9 8 0.984 0.005 0.988
E288_300_Q_11_12 9 0.305 0.037 0.342
E288_400_Q_5_6 5 0.619 0.102 0.721
E288_400_Q_6_7 6 0.234 0.092 0.326
E288_400_Q_7_8 7 0.037 0.102 0.139
E288_400_Q_8_9 8 0.757 0.101 0.857
E288_400_Q_11_12 11 0.595 0.045 0.64
E288_400_Q_12_13 12 0.902 0.022 0.924
E288_400_Q_13_14 12 0.751 0.051 0.802
PHENIX_200 2 2.781 1.832 4.613
STAR_510 7 1.417 0.025 1.443
CDF_RunI 25 0.521 0.058 0.579
CDF_RunII 26 0.926 0.003 0.929
D0_RunI 12 0.647 0.028 0.675
D0_RunII 5 1.021 0.459 1.481
D0_RunIImu 3 3.753 0.284 4.037
LHCb_7TeV 7 1.47 0.271 1.741
LHCb_8TeV 7 0.581 0.067 0.648
LHCb_13TeV 7 1.281 0.038 1.32
CMS_7TeV 4 2.265 0.095 2.361
CMS_8TeV 4 1.98 0.001 1.981
CMS_13TeV_y_0_0.4 14 0.465 0.04 0.505
CMS_13TeV_y_0.4_0.8 14 0.323 0.026 0.349
CMS_13TeV_y_0.8_1.2 14 0.513 0.009 0.522
CMS_13TeV_y_1.2_1.6 14 0.22 0.0 0.22
CMS_13TeV_y_1.6_2.4 14 0.392 0.01 0.402
Total 412 0.84 0.133 0.974
Average-over-replicas \chi^2’s:
Experiment Number of points \chi^2
E605_Q_7_8 7 1.481 \pm 0.321
E605_Q_8_9 8 2.335 \pm 0.381
E605_Q_10.5_11.5 10 0.46 \pm 0.023
E605_Q_11.5_13.5 12 0.941 \pm 0.023
E605_Q_13.5_18 13 1.663 \pm 0.074
E772_Q_5_6 4 1.875 \pm 0.375
E772_Q_6_7 5 1.378 \pm 0.193
E772_Q_7_8 6 3.474 \pm 0.196
E772_Q_8_9 6 3.397 \pm 0.216
E772_Q_11_12 9 0.988 \pm 0.034
E772_Q_12_13 10 1.202 \pm 0.05
E772_Q_13_14 7 2.806 \pm 0.278
E772_Q_14_15 6 0.291 \pm 0.031
E288_200_Q_4_5 4 0.438 \pm 0.218
E288_200_Q_5_6 5 1.499 \pm 0.346
E288_200_Q_6_7 6 0.41 \pm 0.11
E288_200_Q_7_8 7 0.414 \pm 0.179
E288_200_Q_8_9 8 0.678 \pm 0.164
E288_300_Q_4_5 4 0.586 \pm 0.087
E288_300_Q_5_6 5 1.202 \pm 0.204
E288_300_Q_6_7 6 0.539 \pm 0.134
E288_300_Q_7_8 7 0.066 \pm 0.015
E288_300_Q_8_9 8 0.997 \pm 0.09
E288_300_Q_11_12 9 0.377 \pm 0.089
E288_400_Q_5_6 5 0.823 \pm 0.203
E288_400_Q_6_7 6 0.382 \pm 0.115
E288_400_Q_7_8 7 0.172 \pm 0.059
E288_400_Q_8_9 8 0.897 \pm 0.178
E288_400_Q_11_12 11 0.676 \pm 0.106
E288_400_Q_12_13 12 0.947 \pm 0.032
E288_400_Q_13_14 12 0.821 \pm 0.086
PHENIX_200 2 4.431 \pm 1.264
STAR_510 7 1.454 \pm 0.087
CDF_RunI 25 0.588 \pm 0.023
CDF_RunII 26 0.961 \pm 0.083
D0_RunI 12 0.682 \pm 0.013
D0_RunII 5 1.501 \pm 0.123
D0_RunIImu 3 4.062 \pm 0.428
LHCb_7TeV 7 1.773 \pm 0.066
LHCb_8TeV 7 0.681 \pm 0.104
LHCb_13TeV 7 1.342 \pm 0.207
CMS_7TeV 4 2.364 \pm 0.069
CMS_8TeV 4 1.979 \pm 0.095
CMS_13TeV_y_0_0.4 14 0.509 \pm 0.118
CMS_13TeV_y_0.4_0.8 14 0.346 \pm 0.079
CMS_13TeV_y_0.8_1.2 14 0.516 \pm 0.103
CMS_13TeV_y_1.2_1.6 14 0.226 \pm 0.037
CMS_13TeV_y_1.6_2.4 14 0.417 \pm 0.059
Total 412 0.995 \pm 0.011

TMDs in k_\perp or P_\perp space

TMD PDF of the u at Q = 2 GeV and x = 0.001
TMD PDF of the u at Q = 2 GeV and x = 0.01
TMD PDF of the u at Q = 2 GeV and x = 0.1
TMD PDF of the u at Q = 10 GeV and x = 0.001
TMD PDF of the u at Q = 10 GeV and x = 0.01
TMD PDF of the u at Q = 10 GeV and x = 0.1
TMD PDF of the u at Q = 100 GeV and x = 0.001
TMD PDF of the u at Q = 100 GeV and x = 0.01
TMD PDF of the u at Q = 100 GeV and x = 0.1

Data-theory comparison

E605_Q_7_8 data-theory comparison
E605_Q_8_9 data-theory comparison
E605_Q_10.5_11.5 data-theory comparison
E605_Q_11.5_13.5 data-theory comparison
E605_Q_13.5_18 data-theory comparison
E772_Q_5_6 data-theory comparison
E772_Q_6_7 data-theory comparison
E772_Q_7_8 data-theory comparison
E772_Q_8_9 data-theory comparison
E772_Q_11_12 data-theory comparison
E772_Q_12_13 data-theory comparison
E772_Q_13_14 data-theory comparison
E772_Q_14_15 data-theory comparison
E288_200_Q_4_5 data-theory comparison
E288_200_Q_5_6 data-theory comparison
E288_200_Q_6_7 data-theory comparison
E288_200_Q_7_8 data-theory comparison
E288_200_Q_8_9 data-theory comparison
E288_300_Q_4_5 data-theory comparison
E288_300_Q_5_6 data-theory comparison
E288_300_Q_6_7 data-theory comparison
E288_300_Q_7_8 data-theory comparison
E288_300_Q_8_9 data-theory comparison
E288_300_Q_11_12 data-theory comparison
E288_400_Q_5_6 data-theory comparison
E288_400_Q_6_7 data-theory comparison
E288_400_Q_7_8 data-theory comparison
E288_400_Q_8_9 data-theory comparison
E288_400_Q_11_12 data-theory comparison
E288_400_Q_12_13 data-theory comparison
E288_400_Q_13_14 data-theory comparison
PHENIX_200 data-theory comparison
STAR_510 data-theory comparison
CDF_RunI data-theory comparison
CDF_RunII data-theory comparison
D0_RunI data-theory comparison
D0_RunII data-theory comparison
D0_RunIImu data-theory comparison
LHCb_7TeV data-theory comparison
LHCb_8TeV data-theory comparison
LHCb_13TeV data-theory comparison
CMS_7TeV data-theory comparison
CMS_8TeV data-theory comparison
CMS_13TeV_y_0_0.4 data-theory comparison
CMS_13TeV_y_0.4_0.8 data-theory comparison
CMS_13TeV_y_0.8_1.2 data-theory comparison
CMS_13TeV_y_1.2_1.6 data-theory comparison
CMS_13TeV_y_1.6_2.4 data-theory comparison